you can try the guest house(by Columbia) from the pamphlet included in the mail of your testing voucher. But it is very hot, I've been there for my level2 and 1, both times without luck,, called them and said all rooms booked.
so I stayed in a hotel nearby JFK airport, maybe holiday inn express, for one time, and stayed another one by Laguadia, which was Wyndham. Both were good, but the thing is, you have to book long before the test date, otherwise there might be no rooms available or they would be at a very high price. So do the reservation right after you book your flight.
For the JFK, you can take A train, which is an express train to the campus, change to 1-2-3 line at 59 St, maybe, check the metro map online. For Laguadia, even more convenient, you can take M60 bus directly to Columbia campus. It's no hustle for the day because you can have a whole morning to spend,'cause the test will be in the afternoon, always starting at about 1pm. But when it's over, it will be around 5:30 something. So book you return flight as late as possible, maybe 7:30 or 8:00pm, for you are gonna spend at least one hour on the way from Columbia to either airport. 気をつけてください。